This project aims at the development of computational methods to solve the problem posed by the flow of blood in the heart. This problem involves a viscous incompressible fluid (blood) in contact with boundaries (valves and heart muscle) which are moved by the fluid but simultaneously exert forces which alter the fluid motion. Three computational methods are under consideration based on finite differences, vortex dynamics, and an N-particle representation of the fluid. All three methods use a realistic representation of the valves and heart muscle, in which the geometry and physical properties of the heart and valves can be specified by the investigator to any desired accuracy. The principal applications of these methods involve the design of prosthetic valves and artificial hearts, and the testing of hypotheses in cardiac physiology. In particular we aim at the development of a computer test chamber, in which various valve designs can be tested mathematically under controlled conditions which closely simulate those of the living heart. The output of such a test chamber will include a computer generated cine film, showing the detailed motion of the valves, blood, and heart walls as calculated by the computer.